Finite Group Databasebeta

← Group #10710983

Character table — Group #10710983

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1122222224444444444888888888888816161616161616161616161616162424242424242424242424244848
order122344612122224444461224466666121212121244881212121212122424242422444444888888
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111-1-11111-1-1-111-1-1111-1-1111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1
χ61111111111111-1-11111-1-1-111-1-1111-1-1111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111
χ71111111111111-1-11111-1-1-111-1-1111-1-11-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111
χ81111111111111-1-11111-1-1-111-1-1111-1-11-1-111-1-1-1-1-1-11111-1-111-1-1111111-1-1
χ91111-1-11-1-111-1111-1-11-1-11-111-1-1-11-111-1i−ii−i1-1ii−i−iii−i−i1-11-11-11-1ii−i−ii−i
χ101111-1-11-1-111-1111-1-11-1-11-111-1-1-11-111-1i−ii−i1-1ii−i−iii−i−i-11-11-11-11−i−iii−ii
χ111111-1-11-1-111-1111-1-11-1-11-111-1-1-11-111-1−ii−ii1-1−i−iii−i−iii1-11-11-11-1−i−iii−ii
χ121111-1-11-1-111-1111-1-11-1-11-111-1-1-11-111-1−ii−ii1-1−i−iii−i−iii-11-11-11-11ii−i−ii−i
χ131111-1-11-1-111-11-1-1-1-11-11-111111-11-1-1-1-1i−i−ii-11ii−i−i−i−iii1-1-111-1-11ii−i−i−ii
χ141111-1-11-1-111-11-1-1-1-11-11-111111-11-1-1-1-1i−i−ii-11ii−i−i−i−iii-111-1-111-1−i−iiii−i
χ151111-1-11-1-111-11-1-1-1-11-11-111111-11-1-1-1-1−iii−i-11−i−iiiii−i−i1-1-111-1-11−i−iiii−i
χ161111-1-11-1-111-11-1-1-1-11-11-111111-11-1-1-1-1−iii−i-11−i−iiiii−i−i-111-1-111-1ii−i−i−ii
χ172222222222-2-2-2002-2220002-200-2-2-200200000000000000002200-2-2000000
χ182222222222-2-2-2002-2220002-200-2-2-20020000000000000000-2-20022000000
χ19222222222-22-2-222-22222-2-2-2222-2-2222-20000-2-20000000000000000000000
χ20222222222-22-2-2-2-2-2222-222-22-2-2-2-22-2-2-20000220000000000000000000000
χ21222222222-2-22200-2-222000-2-20022-200-2000000000000002200-2-200000000
χ22222222222-2-22200-2-222000-2-20022-200-200000000000000-2-2002200000000
χ232222-2-22-2-22-22-200-222-20002-2002-2200-200000000000000002-200-22000000
χ242222-2-22-2-22-22-200-222-20002-2002-2200-20000000000000000-22002-2000000
χ252222-2-22-2-2-222-2222-22-2-2-22-22-2-22-2-22220000-220000000000000000000000
χ262222-2-22-2-2-222-2-2-22-22-222-2-22222-2-2-2-2200002-20000000000000000000000
χ272222-2-22-2-2-2-2-2200222-2000-2-200-222002000000000000002-200-2200000000
χ282222-2-22-2-2-2-2-2200222-2000-2-200-22200200000000000000-22002-200000000
χ29222-122-1-1-122222222-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000000000
χ30222-122-1-1-122222222-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000000000
χ31222-122-1-1-12222-2-222-1-1-2-2-2-1-111-1-1-111-122-2-211-1-1-1-1111100000000000000
χ32222-122-1-1-12222-2-222-1-1-2-2-2-1-111-1-1-111-1-2-222111111-1-1-1-100000000000000
χ33222-122-1-1-1-22-2-222-22-1-12-2-21-1-1-111-1-1-110000113−33−33−33−300000000000000
χ34222-122-1-1-1-22-2-222-22-1-12-2-21-1-1-111-1-1-11000011−33−33−33−3300000000000000
χ35222-122-1-1-1-22-2-2-2-2-22-1-1-2221-11111-11110000-1-13−33−3−33−3300000000000000
χ36222-122-1-1-1-22-2-2-2-2-22-1-1-2221-11111-11110000-1-1−33−333−33−300000000000000
χ37222-1-2-2-11122-2222-2-2-11-22-2-1-1111-11-1-112i−2i2i−2i-11−i−iii−i−iii00000000000000
χ38222-1-2-2-11122-2222-2-2-11-22-2-1-1111-11-1-11−2i2i−2i2i-11ii−i−iii−i−i00000000000000
χ39222-1-2-2-11122-22-2-2-2-2-112-22-1-1-1-11-111112i−2i−2i2i1-1−i−iiiii−i−i00000000000000
χ40222-1-2-2-11122-22-2-2-2-2-112-22-1-1-1-11-11111−2i2i2i−2i1-1ii−i−i−i−iii00000000000000
χ41222-1-2-2-111-222-2222-2-11-2-221-111-111-1-1-100001-1−i3i3i3−i3−i3i3i3−i300000000000000
χ42222-1-2-2-111-222-2222-2-11-2-221-111-111-1-1-100001-1i3−i3−i3i3i3−i3−i3i300000000000000
χ43222-1-2-2-111-222-2-2-22-2-1122-21-1-1-1-11111-10000-11−i3i3i3−i3i3−i3−i3i300000000000000
χ44222-1-2-2-111-222-2-2-22-2-1122-21-1-1-1-11111-10000-11i3−i3−i3i3−i3i3i3−i300000000000000
χ45444-244-2-2-24-4-4-4004-4-2-2000-220022200-20000000000000000000000000000
χ46444-244-2-2-2-4-44400-4-4-2-20002200-2-220020000000000000000000000000000
χ47444-2-4-4-2224-44-400-44-22000-2200-22-20020000000000000000000000000000
χ48444-2-4-4-222-4-4-440044-2200022002-2-200-20000000000000000000000000000
χ4944-444-444400000000-4-4000000000000000000000000000000000002i−2i2i−2i00
χ5044-444-444400000000-4-400000000000000000000000000000000000−2i2i−2i2i00
χ5144-44-444-4-400000000-44000000000000000000000000000000000002-2-2200
χ5244-44-444-4-400000000-4400000000000000000000000000000000000-222-200
χ5388-8-48-8-4-4-4000000004400000000000000000000000000000000000000000
χ5488-8-4-88-444000000004-400000000000000000000000000000000000000000
χ558-80800-80000004i−4i000000000000004i−4i00000000000000000000000000000
χ568-80800-8000000−4i4i00000000000000−4i4i00000000000000000000000000000
χ578-80-400443−4300004i−4i000000000−2i32i3000−2i2i00000000000000000000000000000
χ588-80-400443−430000−4i4i0000000002i3−2i30002i−2i00000000000000000000000000000
χ598-80-4004−434300004i−4i0000000002i3−2i3000−2i2i00000000000000000000000000000
χ608-80-4004−43430000−4i4i000000000−2i32i30002i−2i00000000000000000000000000000

Here i is the imaginary unit (i² = −1).